The day after what might have been their final debate, the four remaining Republican presidential candidates set their plans Thursday for a nearly two-week sprint across America that could determine who earns the right to square off against President Barack Obama this fall.

A total of 13 states will hold contests through Super Tuesday on March 6. First up: Arizona and Mitt Romney's former home state of Michigan, which have primaries scheduled for next Tuesday.

Expectations are high for Romney in both states, where polls show him neck-and-neck with a surging Rick Santorum.

A Romney loss in Michigan could destroy the former Massachusetts governor's veneer of inevitability and blow the race wide open, analysts say. Top Romney adviser Stuart Stevens promised a win for his candidate in Michigan after Wednesday night's debate.

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Romney stumped for votes in both Arizona and Michigan on Thursday, taking aim at Obama's proposed corporate tax reforms announced this week.

"He has this 'Pollyannish' view that you can take a business and put a lot more taxes on it, and they'll somehow just stay here," Romney told supporters in Milford, Michigan. "Over time they'll go somewhere else. And so I will point out his policies made it harder for this economy to recover."

Romney also pounded away at Santorum, continuing his portrayal of the former Pennsylvania senator as a classic political insider who became addicted to runaway spending during his time in Congress.

"People go to Washington and they vote for things they don't believe in. I mean, one of the candidates last night spent most of the evening describing why it was he voted against his principles," Romney said in direct reference to Santorum, who acknowledged at Wednesday's debate he supported a measure that included an education program he opposed.

For his part, Santorum had no public events scheduled for Thursday following a debate in which he came under regular attack from Romney and Texas Rep. Ron Paul, another presidential contender.

Paul also had no events scheduled for Thursday, but planned appearances in Michigan in coming days.

Former House Speaker Newt Gingrich apparently bypassed Michigan and Arizona, going instead to Washington state and Idaho. Gingrich's strategy relies on winning his former home state of Georgia and other Southern states in the weeks ahead.

On Thursday, Gingrich was the first Republican White House hopeful to criticize Obama for apologizing after Muslim holy books containing extremist language were burned by NATO soldiers.

Gingrich told a crowd in Spokane, Washington, that Obama "apologized for the burning, but I haven't seen the president demand that the government of Afghanistan apologize for the killing of two young Americans."

Gingrich also said Obama was ignoring the threat of radical Muslims intent on harming Americans.

"There seems to be nothing that radical Islamists can do to get Barack Obama's attention in a negative way, and he is consistently apologizing to people who do not deserve the apology of the president of the United States, period," Gingrich said.

Violence erupted in Afghanistan this week after it became public that NATO troops burned Islamic religious materials, including Qurans. In possible response, two American troops were killed Thursday by a man wearing an Afghan National Army uniform.

A statement Thursday from National Security Council spokesman Tommy Vietor said Obama sent a written note to Afghanistan President Hamid Karzai that followed up on a number of issues from recent talks between the two and included an apology for the Quran burnings.

Speaking to reporters aboard Air Force One later Thursday, White House Press Secretary Jay Carney said Republicans who claim the president is weak for apologizing were ignoring basic facts.

"That's a fully false, fallacious and ridiculous narrative that is not borne out by any facts," Carney said.

The fallout from Wednesday night's CNN face-off in Arizona remained unclear, but several analysts were quick to give Romney the edge.

CNN senior political analyst David Gergen said Romney "was the winner by a significant margin," having come in "better prepared" and staying "on offense all night." Erick Erickson of the conservative website RedState.com said Romney "did much better than Santorum." Ari Fleischer, a former spokesman for President George W. Bush, said "it was a good night for" Gingrich and Romney.

Santorum told CNN after the debate that Romney and Paul were "smacking" at him a bit during the night, but that's what comes with doing well in the race. "You fight for that real estate," he said.

On Thursday morning, Romney supporter Rep. Jason Chaffetz, R-Utah, told CNN that his candidate has "connected better than anybody else in the race."

Meanwhile, Santorum campaign spokeswoman Alice Stewart said her candidate has shown "that he has ideas and the record and the views and values that best reflect the conservative party and the conservative people of this country." She explained that's why Santorum is leading nationally and in Michigan.

An American Research Group poll released Thursday shows 38% of likely Michigan GOP primary voters backing Santorum, and 34% supporting Romney -- right on the edge of the survey's margin of error of 4 percentage points. The poll was conducted before Wednesday's debate.

An NBC News-Marist poll released Wednesday showed 37% of likely Michigan primary voters backing Romney and 35% backing Santorum, a difference well within that survey's 3.7 percentage point margin of error.

Paul and Gingrich placed a distant third and fourth in both polls.

A national poll by Quinnipiac University of likely Republican voters released Wednesday showed Santorum leading Romney, 35% to 26%, compared with 14% for Gingrich and 11% for Paul.

Ten states have primaries and caucuses on Super Tuesday on March 6 -- Alaska, Georgia, Idaho, Massachusetts, North Dakota, Ohio, Oklahoma, Tennessee, Vermont and Virginia.